Country music’s Mr. Nice Guy Garth Brooks is turning nasty under the pressure of shocking rape allegations — and is now being slammed in the court of public opinion for publicly identifying his accuser. The 62-year-old “Friends in Low Places” singer put the Mississippi woman right in the crosshairs of his rabid fan base by filing a lawsuit in federal court accusing her of “intentional infliction of emotional distress, defamation, and false light invasion of privacy.” Brooks’ legal salvo comes just days after she walloped him with an explosive lawsuit in Los Angeles Superior Court using the fic…